French trains are run by the SNCF (Société Nationale des Chemins de Fer Français). There are four categories: international overnight/sleeper trains, high-speed trains, intercity trains and local services.
To transport your bike on French trains, the best way is to put it in its own bag; in fact, this is compulsory on certain trains.

Ferries are useful for travellers from Britain, Ireland or countries to the south of France, especially if you plan to bring your own bike with you. Most ferry companies charge a special rate if you’re travelling with a bike.